World champion Pidcock, who won gold in Tokyo, found himself 35 seconds adrift after a front wheel puncture on the fourth of eight laps on the 4.4-kilometre circuit carved in to Elancourt Hill.
Surging with adrenaline, Pidcock sliced into the deficit and hit the front on lap seven and looked set to power ahead.
But Koretzky and South Africa's Alan Hatherly stayed with him to set up a blockbuster final lap.
Koretzky was the first to attack and looked to be set to emulate his compatriot Pauline Ferrand-Prevot who won the women's race on Sunday.
But a mistake allowed Pidcock back in again and then the two riders almost came together on the final rocky descent.
Pidcock then seized his chance and rode clear, crossing the line nine seconds ahead of Koretzky with some fans booing.
Hatherly was third to claim South Africa's first Olympic mountain bike medal.
